In[]:=
g=Graph[{1  2, 1  2, 1  3, 1  3, 2  3, 2  3, 2  4, 2  4, 3  4, 3  4}];
In[]:=
FindEulerianCycle[g]
Out[]=
{{13,34,42,24,43,32,23,31,12,21}}